The number of arrangements of the letters of the word...

There are $5$ vowels in the given word which are $4E ' s \text{ and } 1I$.

Since they have to always occur together we take them as a single object $EEEEI$ for the time being.

This single object together with $7$ remaining object will account for $8$ objects.

There $8$ objects in which there are $3N ' s \text{ and } 2D ' s$ can be arrangement in $\dfrac{8 !}{3 ! 2 !}$ ways.

Corresponding to each of their arrangements the $5$ vowels $E, E, E, E \text{ and } I$ which can be arranged in $\dfrac{5 !}{4 !}$

Hence, required number of arrangements.

$= \dfrac{8 !}{3 ! 2 !} \times \dfrac{5 !}{4 !} = 16800$

Hence this is the correct option.